Workflow to model and texture a jigsaw puzzle
"How would one go about projecting an image across all these individual piece objects? That then get baked into textures? That can then be applied in TTS?"

I would just use the single image as the texture, and each piece would start out being in the same object mesh so that they can all be unwrapped from view at the same time and carry the same material - then you can separate each separate piece with P - 'separate by loose parts'. No baking needed. 

Incidentally, I advise you to increase the resolution of your curve object before converting to mesh if you are concerned about the edges of each piece.